Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 78

The two solutions are complex conjugates.

$x^{2}+6=2x$ $x^{2}-2x+6=0$ To determine the nature of the solutions (without solving), we compute the sign of the discriminant in the quadratic formula ($a=1,\ b=-2,\ c=6$): $b^{2}-4ac=(-2)^{2}-4*1*6=4-24=-20$ Since the discriminant is negative, the two solutions are complex conjugates.